The Dynamics of a Satellite-Gyrostat with a Single Nonzero Component of the Vector of Gyrostatic Moment

Abstract

The dynamics of a satellite-gyrostat moving in the central Newtonian force field along a circular orbit is studied. In the particular case when the vector of gyrostatic moment is parallel to one of the satellite's principal central axes of inertia, all the equilibrium states are determined. For each equilibrium orientation, sufficient conditions of stability are obtained as a result of the analysis of the generalized energy integral, and necessary conditions of stability are determined as a result of analysis of the linearized equations of motion. The evolution of regions of validity for the conditions of stability of equilibrium positions are studied in detail depending on the parameters of the problem. All the bifurcation values of the parameters at which qualitative changes of the regions of stability take place are determined.

Dynamics of a gyrostat satellite with the vector of gyrostatic moment tangent to the orbital plane

“…As mentioned by Sarychev et al (2005), ( 13) and ( 14) need a closer look since they can be valid either for both signs before the square root or for only one sign, which results in the existence of equilibrium positions corresponding to both roots of (12) or only one root (x 2;1 or x 2;2 ). The analysis of the regions of validity of Eqs.…”

“…Saryshev and Mirer (2001) found a new analytical solution of all equilibria for the case where the internal angular momentum of the gyrostat satellite is collinear to its principal axis of inertia. Following the 2001 study, Sarychev et al (2005) determined the bifurcation values and showed the evolution of the regions of validity, for the same particular case, while Sarychev et al (2008) studied the special case where the gyrostatic moment vector lies in one of the satellite's principal central planes of inertia. Molina and Monde ´jar (2004) focused on the motion of a satellite that had, in the first case, spherical symmetry, and in the second case, axial symmetry.…”

Extension of a PID control theory to Lie groups applied to synchronising satellites and drones

“…A satellite gyrostat is made of a suspended rigid body, termed platform , that contains one or more rigid wheels, termed rotors , which are spinning around fixed axes. Normally, it is assumed that the angular velocity of rotation of the rotors with respect to the body of the satellite is quasi‐constant and that the centre of mass of the satellite moves along a circular orbit [35]. Since the total angular velocity must stay constant, a rotation of the wheels causes a global counter‐rotation of the gyrostat, which makes it possible to stabilise its motion (known as principle of momentum transfer [20]).…”

The steady motions of a satellite with a two-degree-of-freedom powered gyroscope in a central gravitational field and their stability

“…4,9,10 In the case of a problem with a rotor, the angle x is a fixed parameter and the equilibrium positions are determined from system It should be noted that it is not advisable to use the above correlation to find the equilibrium positions for the problem with a gyroscope directly from the solutions of the corresponding problem with a rotor. The solutions for the problem with a rotor, the axis of which is parallel to the principal plane of inertia, are determined from equations of the fourth degree.…”

“…All the positions satisfying the sufficient conditions for stability are also determined. The number of them is either equal to 4 or 8 depending on the values of the system parameters.Up to the present time, the problem of the steady motions (equilibrium positions with respect to an orbital basis) of satellites carrying powered rotors has been fairly fully investigated 9,10, etc.). The steady motions of satellites carrying powered gyroscopes have been studied to a lesser extent.…”